Ring authentication method for concurrency environment

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the priority of Korean Patent Application No. 10-2006-0121835 filed on Dec. 4, 2006, and the priority of Korean Patent Application No. 2007-0048106 filed on May 17, 2007, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a ring authentication method for a concurrency environment, the method capable of providing unforgeability, sender anonymity, and deniability in the concurrency environment.

The present invention was supported by the IT R&D program of MIC/IITA. [Project code: 2005-Y-001-02, Project title: Developments of next generation security technology]

2. Description of the Related Art

Message authentication indicates a technology in which, when a sender sends a message to a receiver, the receiver is capable of confirming an identification (ID) of the sender, which should provide unforgeability, sender anonymity, and deniability.

In this case, the unforgeability indicates that an attacker is incapable of disguising as another user, the sender anonymity indicates that receiver is only known that “a sender of a message is one of n number of users.” but a actual sender is unknown, and the deniability indicates that the attacker is incapable of certifying that “a sender and a receiver authenticate a message.” to another user by using an obtained authentication protocol message.

As a message authentication method, a ring authentication method (CRYPTO 2002, refer to p 481-498) is provided by Moni Naor. The ring authentication method uses that a person who knows a private key corresponding to a public key is capable of correctly extracting a plaintext from a ciphertext. The ring authentication method is formed in such a way that only a person who knows a private key corresponding to at least on public key of several public keys is capable of knowing a correct plaintext.

However, in real life, several sessions may be concurrently performed. The ring authentication method is incapable of providing the deniability when the receiver performs protocols with several senders at the same time.

To provide the deniability in a concurrency environment, a ring authentication method using a ring signature and a chameleon hash function is proposed by Susilio and Mu (ICISC 2003, refer to p386-401). The method proposed by Susilio and Mu uses the ring signature and allows a receiver to know that one user belonging to a certain user set signs. According to the method, a message sender may deny “a message m is authenticated” with respect to a certain message. However, a fact that “a message is authenticated” is incapable of being denied. Accordingly, perfect deniability is not provided.

SUMMARY OF THE INVENTION

An aspect of the present invention provides a ring authentication method for a concurrency environment, the method capable of providing unforgeability, sender anonymity, and perfect deniability in the concurrency environment.

According to an aspect of the present invention, there is provided a ring authentication method for a concurrency environment, the method including: requesting a sender of a message to certify the message, the requesting is performed by a receiver receiving the message; sending a message certification value certifying that the sender is one of a plurality of users {P₁, . . . , P_n} and authenticates the message, from the sender requested to certify the message to the receiver by using a signature of proof of knowledge; and verifying the sent message certification value and checking whether the message is authenticated, the verifying and checking is performed by the receiver.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and other advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawing, in which:

<figref idrefs="DRAWINGS">FIG. 1</figref> is a flowchart illustrating a ring authentication method in a concurrency environment according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. Only, in describing operations of the exemplary embodiments in detail, when it is considered that a detailed description on related well-known functions or constitutions unnecessarily may make essential points of the present invention be unclear, the detailed description will be omitted.

In the drawings, the same reference numerals are used throughout to designate the same or similar components.

The present invention may allow a receiver to check that a message m is authenticated by one of users in a predetermined group by using a signature of proof of knowledge, thereby providing sender anonymity simultaneously with perfect deniability.

Hereinafter, to help understanding a ring authentication method according to an exemplary embodiment of the present invention, the signature of proof of knowledge will be described.

Hereinafter, a group generator of a group G whose order is a decimal q is g. A signature of proof of knowledge according to an exemplary embodiment of the present invention is SPK_OR, which is capable of certifying that a sender knows one or more discrete logarithms of discrete logarithm values {log_g(y₁), . . . , log_g(y_n)} when a set of elements of a certain group is {y₁, . . . , y_n}.

For example, it is assumed that the sender knows x_i*=log_g(y_i*).

In the signature of proof of knowledge, the sender sends σ=(c₁, . . . , c_n,s₁, . . . , s_n) to a receiver calculated by Equation 1. <br />σ=(<i>c</i>₁<i>, . . . , c</i>_n<i>,s</i>₁<i>, . . . , s</i>_n)=<i>SPK</i>_OR[(α):<i>y</i>₁<i>=g</i>^α<i>V . . . Vy</i>_n<i>=g</i>^α](m)  Equation (1)

To generate σ, the sender randomly selects r_iand (c_i,s_i) (1≦i(≠i*)≦n) and calculates c by using Equation 2. <br /><i>c=H</i>(<i>m∥y</i>₁<i>∥ . . . ∥y</i>_n<i>∥y</i>₁^c^{<sub2>1</sub2>}<i>g</i>^s^{<sub2>1</sub2>}<i>∥ . . . ∥g</i>^r^{<sub2>i*</sub2>}<i>∥ . . . ∥y</i>_n^c^{<sub2>n</sub2>}<i>g</i>^s^{<sub2>n</sub2>})  Equation (2)

c_i*satisfying

<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mrow><mi>c</mi><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><msub><mi>c</mi><mi>i</mi></msub></mrow></mrow></math></maths><br /> is calculated, and s_i*=r_i*−c_i*x_i*is calculated.

On the other hand, the receiver receiving the received σ checks whether the received σ satisfies following Equation 3, thereby certifying that σ=(c₁, . . . , c_n,s₁, . . . , s_n)=SPK_OR[(α):y₁=g^αV . . . Vy_n=g^α](m). <br />(<i>c</i>₁<i>+ . . . +c</i>_n)mod <i>q=H</i>(<i>m∥y</i>₁<i>∥ . . . ∥y</i>_n<i>∥y</i>₁^c^{<sub2>1</sub2>}<i>g</i>^s^{<sub2>1</sub2>}<i>∥ . . . ∥y</i>_n^c^{<sub2>n</sub2>}<i>g</i>^s^{<sub2>n</sub2>})  Equation (3)

That is, the receiver may certify that the sender knows one or more discrete logarithms x_i*=log_g(y_i*) of discrete logarithm values {log_g(y₁), . . . , log_g(y_n)}.

Hereinafter, the ring authentication method using the described signature of proof of knowledge will be described with reference to <figref idrefs="DRAWINGS">FIG. 1</figref>.

In the ring authentication method according to an exemplary embodiment of the present invention, it is assumed that users P_isending and receiving a message with another user have a private key/public key pair (x_i,y_i=g^x^{<sub2>1</sub2>}), respectively.

A sender, via the present invention, certifies that “The sender is one of {P_i_{<sub2>1</sub2>}, . . . , P_i_{<sub2>n</sub2>}} authenticates a message m.” to a receiver, thereby providing sender anonymity simultaneously with perfect deniability.

Referring to <figref idrefs="DRAWINGS">FIG. 1</figref>, a receiver R receives a message m from a sender P_iin S<b>11</b> and generates a one-time private key/public key pair (x_R,y_R=g^x^{<sub2>R</sub2>}) to authenticate the message m in S<b>12</b>.

In S<b>13</b>, a receiver certification value σ_Rcertifying that the generated private key/public key pair is known is generated as shown in following Equation 4. <br />σ_R<i>=SPK</i>_OR[(α):<i>y</i>_R<i>=g</i>^x^{<sub2>R</sub2>}](<i>m</i>)  Equation (4)

In S<b>14</b>, the generated (y_R,σ_R=SPK_OR[(α):y_R=g^x^{<sub2>R</sub2>}](m)) is sent to the sender P_iand requests message certification.

The sender P_ireceiving the (y_R,σ_R=SPK_OR[(α):y_R=g^x^{<sub2>R</sub2>}](m)) verifies σ_Rsent from the receiver R and checks the truth of σ_Rin S<b>15</b>. σ_Ris verified by using Equation 3 described above.

As a result of the checking, when σ_Ris correct, the sender P_igenerates a message certification value σ_sσ_s=(c₁, . . . , c_n,s₁, . . . , s_n)=SPK_OR[(α):y₁=g^αV . . . Vy_n=g^αVy_R=g^α](m) for satisfying that one of private key/public key pairs of users is known by using a private key/public key pair (x_i,y_i=g^x^{<sub2>i</sub2>}) of the sender P_iaccording to Equation 1 in S<b>16</b>, and sends the generated σ_sto the receiver R in S<b>17</b>.

The receiver R verifies the truth of the σ_ssent from the sender P_iby using Equation 3 in S<b>18</b>.

As a result of the verifying, when σ_sis correct, the receiver R accepts that “The sender P_iis one of {P_i_{<sub2>1</sub2>}, . . . , P_i_{<sub2>n</sub2>}} and authenticates the message m.” in S<b>19</b>.

Via this, the receiver R may provide perfect deniability simultaneously with authenticating the message m in a concurrency environment, in which sender anonymity may be provided.

As described above, according to an exemplary embodiment of the present invention, when authenticating a message in a concurrency environment, perfect deniability is provided simultaneously with providing unforgeability and sender anonymity. In addition, the ring authentication method according to an exemplary embodiment of the present invention is capable of being embodied as a two-round, thereby providing efficiency similar to or higher than conventional methods.

While the present invention has been shown and described in connection with the exemplary embodiments, it will be apparent to those skilled in the art that modifications and variations can be made without departing from the spirit and scope of the invention as defined by the appended claims.